www.iap.uni-jena.de

Optical Design with Zemax

Lecture 10: Illumination

2013-01-15

Herbert Gross

Winter term 2012

2 10 Illumination

Time schedule

1 16.10. Introduction

Introduction, Zemax interface, menues, file handling, preferences, Editors, updates, windows,

Coordinate systems and notations, System description, Component reversal, system insertion,

scaling, 3D geometry, aperture, field, wavelength

2 23.10. Properties of optical systems I Diameters, stop and pupil, vignetting, Layouts, Materials, Glass catalogs, Raytrace, Ray fans

and sampling, Footprints

3 30.10. Properties of optical systems II Types of surfaces, Aspheres, Gratings and diffractive surfaces, Gradient media, Cardinal

elements, Lens properties, Imaging, magnification, paraxial approximation and modelling

4 06.11. Aberrations I Representation of geometrical aberrations, Spot diagram, Transverse aberration diagrams,

Aberration expansions, Primary aberrations,

5 13.+27.11. Aberrations II Wave aberrations, Zernike polynomials, Point spread function, Optical transfer function

6 04.12. Advanced handling

Telecentricity, infinity object distance and afocal image, Local/global coordinates, Add fold

mirror, Vignetting, Diameter types, Ray aiming, Material index fit, Universal plot, Slider,IO of

data, Multiconfiguration, Macro language, Lens catalogs

7 11.12. Optimization I Principles of nonlinear optimization, Optimization in optical design, Global optimization

methods, Solves and pickups, variables, Sensitivity of variables in optical systems

8 18.12. Optimization II Systematic methods and optimization process, Starting points, Optimization in Zemax

9 08.01 Imaging Fundamentals of Fourier optics, Physical optical image formation, Imaging in Zemax

10 15.01. Illumination Introduction in illumination, Simple photometry of optical systems, Non-sequential raytrace,

Illumination in Zemax

11 22.01. Correction I

Symmetry principle, Lens bending, Correcting spherical aberration, Coma, stop position,

Astigmatism, Field flattening, Chromatical correction, Retrofocus and telephoto setup, Design

method

12 29.01. Correction II Field lenses, Stop position influence, Aspheres and higher orders, Principles of glass

selection, Sensitivity of a system correction, Microscopic objective lens, Zoom system

13 05.02. Physical optical modelling Gaussian beams, POP propagation, polarization raytrace, coatings

1. Photometry

2. Energy transport in optical systems

3. Vignetting

4. Non-sequential raytrace

5. Illumination in Zemax

3 10 Illumination

Contents

Illumination systems:

Different requirements: energy transfer efficiency, uniformity

Performnace requirements usually relaxed

Very often complicated structures components

Problem with raytracing: a ray corresponds to a plane wave with infinity extend

Usual method: Monte-Carlo raytrace

Problems: statistics and noise

Illumination systems and strange components needs often a strong link to CAD data

There are several special software tools, which are optimized for (incoherent) illumination:

- LightTools

- ASAP

- FRED

4 10 Illumination

Illumination

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Radiometric vs Photometric Units

Quantity Formula Radiometric Photometric

Term Unit Term Unit

Energy Energy Ws Luminous Energy Lm s

Power

Radiation flux

W

Luminous Flux Lumen Lm

Power per area and solid angle

Ld

d dA

2

cos

Radiance W / sr /

m2

Luminance cd / m

2

Stilb

Power per solid angle

dAL

d

dI

Radiant Intensity W / sr

Luminous Intensity Lm / sr,

cd

Emitted power per area

dLdA

dE cos

Radiant Excitance W / m2

Luminous Excitance Lm / m2

Incident power per area

dLdA

dE cos

Irradiance W / m2

Illuminance Lux = Lm / m

2

Time integral of the power per area

H E dt

Radiant Exposure Ws / m2

Light Exposure Lux s

5

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Photometric Quantities

Radiometric quantities:

Physical MKSA units, independent of receiver

Photometric quantities:

Referenced on the human eye as receiver

Conversion by a factor Km

Sensitivity of the human eye V(l)

for photopic vision (daylight)

ll l )(VKmV

W

LmKm 673

V(l )

l400 450 500 550 600 650 700 750

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Illuminance description

1 Lux just visible

50 - 100 Lux coarse work

100 Lux projection onto

screen

100 - 300 Lux fine work

1000 Lux finest work

100000 Lux sunlight on paper

6

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Solid Angle

ddA

r

dA

r

cos

2 2

2D extension of the definition of an angle:

area perpendicular to the direction over square of distance

Area element dA in the distance r with inclination

Units: steradiant sr

Full space: = 4p

half space: = 2p

Definition can be considered as

cartesian product of conventional angles

source point

d

rdA

n

yxr

dy

r

dx

r

dAd

2

7

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Irradiance

Irradiance: power density on a surface

Conventional notation: intensity

Unit: watt/m2

Integration over all incident directions

Only the projection of a collimated beam

perpendicular to the surface is effective

dLdA

dE cos

cos)( 0 EE

A

A

E()

Eo

8

d

s

dAS

S

n

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Differential Flux

Differential flux of power from a

small area element dAs with

normal direction n in a small

solid angle dΩ along the direction

s of detection

Integration of the radiance over

the area and the solid angle

gives a power

S

SS

S

AdsdL

dAdL

dAdLd

cos

2

PdA

A

9

Radiance independent of space coordinate

and angle

The irradiance varies with the cosine

of the incidence angle

Integration over half space

Integration of cone

Real sources with Lambertian

behavior:

black body, sun, LED

constLsrL

,

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Lambertian Source

p 2sin)( ALLam

coscos oEALE

LAdEHR

Lam p )(

E()

x

z

L

x

z

10

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Fundamental Law of Radiometry

Differential flux of power from a

small area element dAS on a

small receiver area dAR in the

distance r,

the inclination angles of the

two area elements are S and

R respectively

Fundamental law of radiometric

energy transfer

The integration over the geometry gives the

total flux

ESES

ES

dAdAr

L

dAdAr

Ld

coscos2

2

2

z

s

s

xs

ys

source

receiver

xR

yR

zR

AS

r

ns

AR

nR

S

R

11

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Radiation Transfer

Basic task of radiation transfer problems:

integration of the differential flux transfer law

Two classes of problems:

1. Constant radiance, the integration is a purely geometrical task

2. Arbitrary radiance, a density function has to be integrated over the geometrical light tube

Special cases:

Simple geometries, mostly high symmetric , analytical formulas

General cases: numerical solutions

- Integration of the geometry by raytracing

- Considering physical-optical effects in the raytracing:

1. absorption

2. reflection

3. scattering

ESESES dAdAr

LdAdA

r

Ld coscos

22

2

12

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Transfer of Energy in Optical Systems

Conservation of energy

Differential flux

No absorption

Sine condition fulfilled

d d2 2 '

ddudAuuLd cossin2

T 1

y

dA dA's's

EnP ExP

n n'

F'F

y'

u u'

'sin''sin uynuyn

13

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Transfer of Energy in Optical Systems

Aplanatic systems:

sine condition fulfilled

consequence: constant radiance

Irradiance

Irradiance in afocal systems

Irradiance changes with the square of the numerical aperture

Optical systems with finite image location:

m: magnification

mP: magnification of pupil imaging

Approximation mp = 1:

n x n xsin ' 'sin '

L

n

L

n2 2

'

'

p 2sin LE

2

2

4

''

F

L

n

nE

p

P

P

AP

m

mF

mmf

Du

12

1

'2'sin

222

2

1

'

14

')('

m

E

mF

L

n

nmE

p

14

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Illumination Fall-off

Irradiance decreases in the image field

Two reasons:

1. projection due to oblique ray bundles

2. enlarged distances along oblique chief rays

Natural vignetting: smooth function

depends on: 1. stop location

2. distortion correction

entrance

pupil

y yp

chief ray

chief ray

exit

pupil

y' y'p

w'

w

R'Ex

U

axis bundle

off axis

bundle

marginal

ray

E(y) E(y')U'

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Natural Vignetting: Setup with Rear Stop

Stop behind system:

exact integration possible

Special case on axis

Approximation small aperture:

Classical cos-to-the-fourth-law

2/1

222

222

'tan'cos1

'tan'cos411

'

2)'(

uw

uw

n

nLwE

p

'sin'

'sin')0(' 2

2

2 uLn

nuLE

pp

'cos)0()'( 4 wEwE

AP

u'w'

rw

ro

w'

16

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Illumination Fall-off due to Natural Vignetting

w

cos4w

0

1

10°

0.94

20°

0.78

30°

0.56

w

cos w'4

Relative decrease of irradiance towards the rim of the field

17

10 Illumination

Real Systems: Vignetting

Artificial vignetting by

truncation of rays

Change of usable pupil area

due to lens diameters, stops,...

Approximation for uniform

illuminated pupils:

irradiance decreases proportional

to effective pupil area E(w)

w

pupil area

field angle

clear

obstructed

clearclear

obstructed

E(0)

18

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Photometry in Phase Space

Radiation transport in optical systems

Phase space area changes its shape

Finite chief ray angle:

parallelogram geometry y

p

2y

2y'

2sinu

2sinu'

sinw'

y

y'

s'

Uw' U'

y

y'

s

lens stop

19

Conventional raytrace:

- the sequence of surface hits of a ray is pre-given and is defined by the index vector

- simple and fast programming of the surface-loop of the raytrace

Non-sequential raytrace:

- the sequence of surface hits is not fixed

- every ray gets ist individual path

- the logic of the raytrace algorithm determines the next surface hit at run-time

- surface with several new directions of the ray are allowed:

1. partial reflection, especially Fresnel-formulas

2. statistical scattering surfaces

3. diffraction with several grating orders or ranges of deviation angles

Many generalizations possible:

several light sources, segmented surfaces, absorption, …

Applications:

1. illumination modelling

2. statistical components (scatter plates)

3. straylight calculation

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Non-sequential raytrace

Signal

1 2 3 4

Reflex 1 - 2

Reflex 3 - 2

1

2

3

1. Prism with total internal

reflection

2. Ghost images in optical systems

with imperfect coatings

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Non-sequential raytrace

3. Illumination systems, here:

- cylindrical pump-tube of a solid state laser

- two flash lamps (A, B) with cooling flow tubes (C, D)

- laser rod (E) with flow tube (F, G)

- double-elliptical mirror

for refocussing (H)

Different ray paths

possible

A: flash lamp gas

H

4

B: glass tube of

lamp

C: water cooling

D: glass tube of cooling

5

6

3

2

1

7

E: laser rod

F: water cooling

G: glass tube of cooling

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Non-sequential raytrace

Simple options:

Relative illumination / vignetting for systems with rotational symmetry

Advanced possibility:

- non-sequential component

- embedded into sequential optical systems

- examples: lightguide, arrays together with focussing optics, beam guiding,...

General illumination calculation:

- non-sequential raytrace with complete different philosophy of handling

- object oriented handling: definition of source, components and detectors

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Illumination in Zemax

Relative illumination or vignetting plot

Transmission as a function of the field size

Natural and arteficial vignetting are seen

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Relative Illumination

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25

y field in °

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

relative

illumination

natural vignetting

cos4 w

onset of

truncation

total

illumination

vignetting

Partly non-sequential raytrace:

Choice of surface type ‚non-sequential‘

Non-sequential component editor with many control parameters is used to describe the

element:

- type of component

- reference position

- material

- geometrical parameters

Some parameters are used from the lens data editor too:

entrance/exit ports as interface planes to the sequential system parts

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Illumination in Zemax

Example:

Lens focusses into a rectangular lightpipe

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Illumination in Zemax

Complete non-sequential raytrace

Switch into a different control mode in File-menue

Defining the system in the non-sequential editor, separated into

1. sources

2. light guiding components

3. detectors

Various help function are available to

constitue the system

It is a object (component) oriented philosophy

Due to the variety of permutations, the raytrace

is slow !

27 10 Illumination

Illumination in Zemax

Many types of components and options are available

For every component, several

parameters can be fixed:

- drawing options

- coating, scatter surface

- diffraction

- ray splitting

- ...

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Illumination in Zemax

Starting a run requires several control

parameters

Rays can be accumulated

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Illumination in Zemax

Typical output of a run:

30 10 Illumination

Illumination in Zemax